Superconducting Signal Amplifier

ABSTRACT

A system includes a first superconducting wire and a second superconducting wire connected in parallel. The system includes a first current source coupled to the first superconducting wire and configured to supply a first current in response to a trigger event. The system includes a second current source coupled in series with the parallel combination of the first superconducting wire and the second superconducting wire and configured to supply a second current. The superconducting wires are configured to, while receiving the second current, operate in a superconducting state in the absence of the first current. The first superconducting wire is configured to, while receiving the second current, transition to a non-superconducting state in response to the first current. The second superconducting wire is configured to, while receiving the second current, transition to a non-superconducting state in response to the first superconducting wire transitioning to the non-superconducting state.

PRIORITY AND RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/028,288, filed Jul. 5, 2018, which is a continuation of International(PCT) Application No. PCT/US2018/033042, filed May 16, 2018, entitled“Superconducting Signal Amplifier,” which claims priority to U.S.Provisional Application No. 62/507,193, filed May 16, 2017, entitled“Cascaded Superconducting Signal Amplifier;” U.S. ProvisionalApplication No. 62/572,874, filed Oct. 16, 2017, entitled “CascadedSuperconducting Signal Amplifier;” and U.S. Provisional Application No.62/520,447, filed Jun. 15, 2017, entitled “Niobium-GermaniumSuperconducting Photon Detector,” each of which is incorporated byreference herein in its entirety.

TECHNICAL FIELD

This relates generally to signal amplifiers, including but not limitedto, superconducting signal amplifiers.

BACKGROUND

Signal amplifiers are widely used in electronic devices, such as audiosignal amplifiers, video signal amplifiers, communication signalamplifiers, power amplifiers, etc. Performance of signal amplifiersbased on conventional transistors is limited by the operationcharacteristics of the conventional transistors, such as leakagecurrent, noise, switching speed, and thermal dissipation.

Superconductors are materials capable of operating in a superconductingstate with zero electrical resistance under particular conditions.

SUMMARY

Accordingly, there is a need for systems and/or devices with moreefficient and effective signal amplifiers and methods for operatingthem. Such systems, devices, and methods for making and/or using themoptionally complement or replace conventional systems, devices, andmethods for making and/or using thereof.

However, in superconductor circuits, leakage current, heating, andcurrent swapping problems can limit the effectiveness of thesuperconducting circuits. For example, leakage current intosuperconducting nanowires as well as current-swapping betweensuperconducting nanowires has limited the performance of superconductoramplifier circuits.

As described herein, by controlling the location of an initialperturbation (e.g., small induction) and current redistribution to theclosest neighboring channel(s), parallel nanowires are configured toswitch sequentially rather than in parallel. This sequential avalanchescheme allows the use of a large number of parallel nanowires in anamplifier circuit and provides increased gain and performance.

Additionally, many superconductors require very low temperatures tooperate in a superconducting state. However, operating superconductingcircuitry at these low temperatures can be challenging. Achievingtemperatures near absolute zero (e.g., via the use of lasers and/ormagnetic fields), such as less than 1 Kelvin, 1-2 Kelvin, or 2-3 Kelvin,often requires high performance cooling systems that are large andcostly. In particular, the challenges become significant as the desiredtemperature approaches zero. In addition, it is difficult to maintainthe near-zero temperature due to high cooling power needed for reliableoperation of many superconducting circuits. Therefore, there is a greatneed for superconducting circuitry that is capable of operating in asuperconducting state at higher temperatures (e.g., 3-4 Kelvin, 4-5Kelvin, 5-10 Kelvin, etc.). The present disclosure describes variousembodiments of such superconducting circuitry.

In one aspect, some embodiments include an electronic system having: (1)a first circuit that includes a plurality of superconducting wires(e.g., two or more superconducting wires, such as two, three, four, ormore superconducting wires) connected in parallel with one another, theplurality of superconducting wires including: (a) a firstsuperconducting wire with a corresponding first thresholdsuperconducting current; and (b) a second superconducting wire; and (2)a second circuit (e.g., a readout circuit) connected in parallel to thefirst circuit; (3) a first current source (e.g., an input currentsource) connected to the first superconducting wire and configured toselectively supply a first current (e.g., an input current); and (4) asecond current source (e.g., an amplification current source) connectedto a combination of the first circuit and the second circuit andconfigured to supply a second current (e.g., an amplification current)so that the plurality of superconducting wires operate in asuperconducting state (e.g., in the absence of additional current, suchas the first current), whereby supplying the first current to the firstsuperconducting wire with the first current source causes at least thefirst superconducting wire to cease to operate in the superconductingstate and subsequently causes the second superconducting wire to ceaseto operate in the superconducting state.

In another aspect, some embodiments include a method, comprising: (1)providing an amplification current to a first circuit that includes aplurality of superconducting wires connected in parallel with oneanother, the amplification current causing the plurality ofsuperconducting wires to operate in a superconducting state; (2) whilethe plurality of superconducting wires are operating in thesuperconducting state, supplying an additional current to a firstsuperconducting wire of the plurality of superconducting wires so thatcurrent supplied to the first superconducting wire exceeds a firstthreshold superconducting current of the first superconducting wire; (3)in response to supplying the additional current to the firstsuperconducting wire, transitioning the first superconducting wire fromthe superconducting state to a non-superconducting state; (4) subsequentthe transition of the first superconducting wire from thesuperconducting state to the non-superconducting state: (a) sequentiallytransitioning the remainder of the superconducting wires of theplurality of superconducting wires from the superconducting state to thenon-superconducting state; and (b) directing the amplification currentto a second circuit that is connected in parallel to the first circuit.

In yet another aspect, some embodiments include an electronic devicehaving a plurality of superconducting wires connected in parallel withone another, the plurality of superconducting wires including: (1) afirst superconducting wire having a first threshold superconductingcurrent; and (2) a second superconducting wire having a second thresholdsuperconducting current that is greater than the first thresholdsuperconducting current.

In yet another aspect, some embodiments include a method for fabricationof a superconducting circuit. The method including: (1) depositing athin film of a superconducting material over a substrate; and (2)removing (e.g., etching) one or more (e.g., two or more) portions of thethin film to define a plurality of superconducting wires, the pluralityof superconducting wires including: (a) a first superconducting wirewith a corresponding first threshold superconducting current; and (b) asecond superconducting wire with a corresponding second thresholdsuperconducting current that is greater than the first thresholdsuperconducting current.

In some embodiments, the superconducting circuits and componentsdescribed herein are composed of niobium-germanium adapted to operate ina superconducting state at temperatures above 3 Kelvin (e.g., 3.1 Kelvinto 6 Kelvin).

Thus, devices and systems are provided with methods for fabricating andoperating superconducting circuitry, thereby increasing theeffectiveness, efficiency, and user satisfaction with such systems anddevices.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the various described embodiments,reference should be made to the Detailed Description below, inconjunction with the following drawings in which like reference numeralsrefer to corresponding parts throughout the figures.

FIGS. 1A-1E are block diagrams illustrating representativesuperconducting circuits in accordance with some embodiments.

FIGS. 2A-2B are block diagrams illustrating representativesuperconducting circuits having a constriction point in accordance withsome embodiments.

FIGS. 3A-3G are prophetic diagrams illustrating a representativeoperating sequence of the superconducting circuit of FIG. 2B inaccordance with some embodiments.

FIG. 4 is a circuit diagram illustrating a representativesuperconducting circuit in accordance with some embodiments.

FIGS. 5A-5G are prophetic diagrams illustrating a representativeoperating sequence of the superconducting circuit of FIG. 2B inaccordance with some embodiments.

FIGS. 6A-6B are block diagrams illustrating representative components ofa superconducting circuit in accordance with some embodiments.

FIGS. 7A-7C are cross-sectional diagrams illustrating a representativefabrication sequence for a superconducting wire in accordance with someembodiments.

FIG. 8 is a cross-sectional diagram illustrating a representativelayering for a superconducting wire in accordance with some embodiments.

FIGS. 9A-9B are block diagrams illustrating a photonic circuit thatemploys a superconducting wire in accordance with some embodiments.

FIGS. 10A-10B show the results of a numerical simulation of asuperconducting circuit in accordance with some embodiments.

DETAILED DESCRIPTION

Reference will now be made in detail to embodiments, examples of whichare illustrated in the accompanying drawings. In the following detaileddescription, numerous specific details are set forth in order to providea thorough understanding of the various described embodiments. However,it will be apparent to one of ordinary skill in the art that the variousdescribed embodiments may be practiced without these specific details.In other instances, well-known methods, procedures, components,circuits, and networks have not been described in detail so as not tounnecessarily obscure aspects of the embodiments.

Many modifications and variations of this disclosure can be made withoutdeparting from its spirit and scope, as will be apparent to thoseskilled in the art. The specific embodiments described herein areoffered by way of example only, and the disclosure is to be limited onlyby the terms of the appended claims, along with the full scope ofequivalents to which such claims are entitled.

FIGS. 1A-1E are block diagrams illustrating representativesuperconducting circuits in accordance with some embodiments. FIG. 1Ashows a superconducting circuit 100 having a superconducting layer 118(e.g., a thin film or a sheet of one or more superconducting materials,or a layer that includes one or more superconducting materials, such asniobium or niobium alloys), a first current source 102 connected to thesuperconducting layer 118 (optionally via a supply wire 116), a secondcurrent source 104 connected to the superconducting layer 118, andcircuitry 114 coupled to the superconducting layer 118 (optionally viaresistor(s) 112). FIG. 1A also shows electrical ground 110 (electricallycoupled to the superconducting layer 118). In some embodiments, thefirst current source 102 is configured to supply a current for a limitedtime in response a trigger event (e.g., detection of one or morephotons). Supply wire 116 may be formed from a superconducting materialor from a non-superconducting (e.g., metallic) material. In someembodiments, the superconducting layer 118, the current sources 102 and104, and the circuitry 114 are coupled to a common ground (e.g., ground110), while in other embodiments, one or more are coupled to distinctgrounds or reference nodes. In accordance with some embodiments, thesuperconducting layer 118 includes a plurality of wires 106 defined inpart by a plurality of gaps 108. For example, wire 106-1 corresponds tothe section of the superconducting layer 118 between the left edge ofthe gap 108-1 and the left edge of the superconducting layer 118. Asanother example, wire 106-5 corresponds to the section of thesuperconducting layer 118 between the right edge of the gap 108-4 andthe right edge of the superconducting layer 118. As shown in FIG. 1A, insome embodiments, the gaps 108 are aligned on a side nearest to thecurrent source 104. In some embodiments (not shown), the gaps 108 arealigned on a side opposite to the side close to the current source 104.In some embodiments, the gaps 108 are not linearly aligned (e.g., arespective edge of each gap is aligned in accordance with a nonlinearfunction, such as a parabolic equation).

As used herein, a “superconducting circuit” or “superconductor circuit”is a circuit having one or more superconducting materials. For example,a superconductor amplifier circuit is an amplifier circuit that includesone or more superconducting materials. As used herein, a“superconducting” material is a material that is capable of operating ina superconducting state (under particular conditions). For example, asuperconducting material is a material that operates as a superconductor(e.g., operates with zero electrical resistance) when cooled below aparticular temperature (e.g., a threshold temperature) and having lessthan a threshold current flowing through it. A superconducting materialis also called herein a superconduction-capable material. In someembodiments, the superconducting materials operate in an “off” statewhere little or no current is present. In some embodiments, thesuperconducting materials can operate in a non-superconducting stateduring which the materials have a non-zero electrical resistance (e.g.,a resistance in the range of one thousand to ten thousand ohms). Forexample, a superconducting material supplied with a current greater thana threshold superconducting current for the superconducting materialtransitions from a superconducting state having zero electricalresistance to a non-superconducting state having non-zero electricalresistance. As an example, superconducting layer 118 is a layer that iscapable of operating in a superconducting state (e.g., under particularoperating conditions).

As used herein, a “wire” is a section of material configured fortransferring electrical current. In some embodiments, a wire includes asection of material conditionally capable of transferring electricalcurrent. For example, a wire made of a superconducting material that iscapable of transferring electrical current while the wire is maintainedat a temperature below a threshold temperature. As another example, awire made of semiconducting material is capable of transferringelectrical current while the wire is maintained at a temperature above afreeze-out temperature. A cross-section of a wire (e.g., a cross-sectionthat is perpendicular to a length of the wire) optionally has a regular(e.g., flat or round) shape or an irregular shape. While some of thefigures show wires having rectangular shapes, one skilled in the artwould recognize that any shape could be used. In some embodiments, alength of a wire is greater than a width or a thickness of the wire(e.g., the length of a wire is at least 5, 6, 7, 8, 9, or 10 timesgreater than the width and the thickness of the wire). In some cases, awire is a section of the superconducting layer 118 having a width equalto the distance between an edge of the sheet and a gap in the sheet, orbetween two gaps in the sheet, e.g., as shown in FIG. 1A.

In some embodiments, the resistor(s) 112 include one or more distinctcomponents. In some embodiments, the resistor(s) 112 include one or moreresistances inherent in the circuitry 114 and/or the connection betweencircuitry 114 and the superconducting layer 118.

In some embodiments, the circuitry 114 includes a readout circuit. Insome embodiments, the circuitry 114 is configured to measure currentreceived from (or via) the superconducting layer 118.

FIG. 1B shows a superconducting circuit 120 similar to thesuperconducting circuit 100 in FIG. 1A. In FIG. 1B, the superconductinglayer 124 includes a plurality of wires 126 defined at least in part bya plurality of gaps 128. In accordance with some embodiments, the gaps128 in FIG. 1B are aligned at a midpoint.

FIG. 1C shows a superconducting circuit 130 that includes a firstcurrent source 102 connected to the superconducting wire 136-1(optionally via a supply wire 116), a plurality of wires 136, a secondcurrent source 104, and circuitry 114 coupled to the superconductinglayer 118 (optionally via resistor(s) 112). In some embodiments, theplurality of wires 136 are coupled to electrical ground 110. In someembodiments, the wires 136 are all composed of a same superconductingmaterial. In some embodiments, the wires 136 are composed of two or moredistinct superconducting materials. For example, the wire 136-1 iscomposed of a first superconducting material (e.g., niobium) and thewire 136-4 is composed of a second superconducting material that isdistinct from the first superconducting material (e.g., cadmium). Insome embodiments, the wires 136 each have a same width, while in otherembodiments the wires 136 have two or more distinct widths (e.g., thewire 136-1 has a first width and the wire 136-4 has a second width thatis distinct from the first width). In some embodiments, the wires 136each have a geometric shape (e.g., rectangular or oval cross-section),while in other embodiments, one or more of the wires 136 have anon-geometric shape (e.g., irregular cross-section). In someembodiments, the wires 136 each have a rectangular or oval shape (whenviewed from top down as shown in a plan view), while in otherembodiments, one or more of the wires 136 have any other shape. In someembodiments, the wires 136 each have a same thickness, while in otherembodiments, one or more of the wires 136 have a thickness differentfrom others of the wires 136.

FIG. 1D shows a superconducting circuit 140 having a superconductinglayer 148, a first current source 102 connected to the superconductinglayer 148 (optionally via wire 116), a second current source 104connected to the superconducting layer 148, and circuitry 114 coupled tothe superconducting layer 148 (optionally via resistor(s) 112). In someembodiments, the superconducting layer 148 is electrically coupled withelectrical ground 110. In accordance with some embodiments, thesuperconducting layer 148 includes ‘n’ wires 106 defined in part by‘n−1’ gaps 108.

FIG. 1E shows a superconducting circuit 150 having a superconductinglayer 151, a first current source 102 connected to the superconductinglayer 151 (optionally via wire 116), a second current source 104connected to the superconducting layer 151, and circuitry 114 coupled tothe superconducting layer 151 (optionally via resistor(s) 112). In someembodiments, the superconducting layer 151 is electrically coupled withan electrical ground 110. In accordance with some embodiments, thesuperconducting layer 151 includes wires 106 defined in part by gaps152.

In some embodiments, one example of which is shown in FIG. 1E, the gaps152 are configured so as to enable thermal energy to pass betweenadjacent wires 106. In some embodiments, the gaps 152 are configured soas to enable capacitive coupling between adjacent wires 106. In someembodiments, each gap 152 has a width in the range of 5 nm to 20 nms. Insome embodiments, the gaps 152 are composed of a thermally-conductivematerial such as diamond or aluminum nitride (e.g., the gap 152 isfilled with a thermally-conductive material). In some embodiments, thethermally-conductive material in the gap 152 is an electrical insulator(e.g., the thermally-conductive material in the gap 152 is electricallynon-conductive). In some embodiments, the thermally-conductive materialin the gap 152 has a resistance higher than the resistance of adjacentwires 106 in a superconducting state (e.g., the thermally-conductivematerial is a conductor with non-zero resistance, such as 50 Ohms orhigher).

In some embodiments, one or more of the gaps 152 have a regular shapesuch as a rectangle or oval. In some embodiments, one or more of thegaps 152 have an irregular shape. In some embodiments, the gaps 152 haveincreasing lengths such that gap 152-1 is shorter than gap 152-2 and gap152-2 is shorter than gap 152-3. In some embodiments, the gaps 152 havethe same, or substantially the same, length (e.g., within 5%, 10%, or15% of one another). In some embodiments, the wires 106 the same, orsubstantially the same, width (e.g., within 5%, 10%, or 15% of oneanother). In some embodiments, the wires 106 have differing widths. Forexample, the wires 106 have increasing widths such that wire 106-2 iswider than wire 106-1 and wire 106-3 is wider than wire 106-2.

FIGS. 2A-2B are block diagrams illustrating representativesuperconducting circuits having a constriction point in accordance withsome embodiments. FIG. 2A shows a superconducting circuit 200 similar tothe superconducting circuit 100 in FIG. 1A. However, the superconductinglayer 201 in FIG. 2A includes a constriction 202 defined on the wire106-1. FIG. 2A also shows the wire 106-1 having a width of 203 remotefrom the constriction 202 and a width 205 at the point of theconstriction 202. In some embodiments, the constriction 202 is definedby a widening of the gap 108-1 at a point along the length of the wire106-1. In some embodiments, the constriction 202 is anon-superconducting material whose presence narrows the width of thewire 106-1.

FIG. 2B shows a superconducting circuit 210 similar to thesuperconducting circuit 200 in FIG. 2A. However, the constriction 204along the wire 106-1 in FIG. 2B has a triangular shape, rather than thesemi-circular shape of the constriction 202 in FIG. 2A. In someembodiments (not shown), the constriction has another regular shape(e.g., a triangle with one or more rounded corners, a rectangle with orwithout one or more rounded corners), while in other embodiments, theconstriction has an irregular shape.

FIGS. 3A-3G provide a prophetic example illustrating a representativeoperating sequence of the superconducting circuit 210 of FIG. 2B inaccordance with some embodiments. FIG. 3A shows the superconductingcircuit 210 at a first time. As shown in FIG. 3A, at the first time, thecurrent source 104 is supplying an amplification current 302 to thesuperconducting layer 203 and at least a portion of the amplificationcurrent 302 is flowing through each of the wires 106.

FIG. 3B shows the superconducting circuit 210 at a second time (that issubsequent to the first time). As shown in FIG. 3B, at the second time,the current source 104 is still supplying the current 302 and thecurrent source 102 is supplying an additional current 304 (optionallyvia wire 116).

FIG. 3C shows the superconducting circuit 210 at a third time (that issubsequent to the second time). As shown in FIG. 3C, at the third time,at least a portion of the wire 106-1 has transitioned from asuperconducting state to a non-superconducting state as denoted by theregion 306-1. The transition of the wire 106-1 is in response to thecurrent supplied to the wire 106-1 (e.g., a sum of the current 304 and aportion of the current 302 previously flowing through the wire 106-1)exceeding a threshold superconducting current for the wire 106-1 (e.g.,current between 0.5 μA and 10 μA). In some embodiments, the current 304from the current source 102 is adapted (e.g., selected) such that thetotal current supplied to the wire 106-1 (e.g., current 304 plus aportion of current 302) exceeds the threshold superconducting currentfor the wire 106-1.

In the non-superconducting state, the wire 106-1 has a non-zeroelectrical resistance and thus the current substantially ceases to flowthrough the wire 106-1 (e.g., less than 10%, 5%, or 1% of the currentcontinues to flow through the wire 106-1) while at least one of theother wires 106 continues to have zero electrical resistance. Thecurrent that has previously flown through the wire 106-1 (e.g., thecurrent 304 and/or a portion of the current 302) is redirected throughthe other wires 106. In some embodiments, the current source 102continues to supply the current 304 after the wire 106-1 hastransitioned to the non-superconducting state, while in otherembodiments, the current source 102 ceases to supply the current 304after the wire 106-1 has transitioned to the non-superconducting state.

FIG. 3D shows the superconducting circuit 210 at a fourth time (that issubsequent to the third time). As shown in FIG. 3D, at the fourth time,the wire 106-2 has transitioned from a superconducting state to anon-superconducting state as denoted by the region 306-2. The transitionof the wire 106-2 is in response to the current supplied to the wire106-2 exceeding a threshold superconducting current for the wire 106-2(e.g., due to the additional current redirected from wire 106-1).

FIG. 3E shows the superconducting circuit 210 at a fifth time (that issubsequent to the fourth time). As shown in FIG. 3E, at the fifth time,the wire 106-3 has transitioned from a superconducting state to anon-superconducting state as denoted by the region 306-3 in response toadditional current redirected from the wires 106-1 and 106-2. Thetransition of wire 106-3 is in response to the current supplied to thewire 106-3 exceeding a threshold superconducting current for the wire106-3.

FIG. 3F shows the superconducting circuit 210 at a sixth time (that issubsequent to the fifth time). As shown in FIG. 3F, at the sixth time,the wire 106-4 has transitioned from a superconducting state to anon-superconducting state as denoted by the region 306-4 in response toadditional current redirected from the wires 106-1, 106-2, and 106-3.The transition of wire 106-4 is in response to the current supplied tothe wire 106-4 exceeding a threshold superconducting current for thewire 106-4.

FIG. 3G shows the superconducting circuit 210 at a seventh time (that issubsequent to the sixth time). As shown in FIG. 3G, at the seventh time,the wire 106-5 has transitioned from a superconducting state to anon-superconducting state as denoted by the region 306-5 in response toadditional current redirected from the other wires 106. The transitionof wire 106-5 is in response to the current supplied to the wire 106-5exceeding a threshold superconducting current for the wire 106-5.

In response to all of the wires 106 transitioning to thenon-superconducting state, current 308 (e.g., some or all of current302) from the current source 104 is directed (optionally through theresistor(s) 112) to the circuitry 114. In some embodiments, theresistance of the resistor(s) 112 is less than a combined resistance ofthe wires 106 when the wires are in the non-superconducting state, whichfacilitates a large portion of the current 308 to flow to the circuitry114.

As described above with respect to FIGS. 3A-3G, providing the inputcurrent to the first wire 106-1 causes a sequential (or near sequential)cascade effect through the superconducting circuit (e.g., a sequentialtransition of wires 106-1 through 106-5 from superconducting states tonon-superconducting states) which in turn redirects current from thesecond current source 104 to the circuitry 114. Typically, the currentprovided by the second current source 104 is greater than the currentprovided by the first current source 102 (e.g., the current provided bythe second current source 104 is at least 4, 5, 6, 7, 8, 9, or 10 timesgreater than the current provided by the first current source 102).Thus, the electronic systems illustrated in FIGS. 3A-3G operate as anamplifier (e.g., a current amplifier) for the first current source inthat the current 308 in FIG. 3G is larger than the current 304 in FIG.3B.

FIG. 4 is a circuit diagram illustrating a representativesuperconducting circuit in accordance with some embodiments. FIG. 4shows a circuit 400 equivalent to the block diagrams of FIGS. 1A-1D. InFIG. 4, the circuit 400 includes a voltage source 424 with inputresistance 402 (e.g., equivalent to current source 102 in FIG. 1A),current source 401 (e.g., equivalent to current source 104 in FIGS. 1A,3A, etc.), an optional resistor 418 (e.g., corresponding to resistor112), and the circuitry 114. FIG. 4 also shows inductors 404, 406, 408,and 410 representing inductances of the superconducting wires in FIGS.1A-1D, 2A-2B, and 3A-3G. For example, inductors 404 and 406 correspondto wire 106-1 in FIG. 1D and inductor 410 corresponds to wire 106-n inFIG. 1D, whereas inductor 408 corresponds to a wire between 106-1 and106-n, such as wire 106-2.

FIGS. 5A-5G are prophetic diagrams illustrating a representativeoperating sequence of a superconducting circuit 501 in accordance withsome embodiments. The superconducting circuit 501 comprises thesuperconducting circuit 150 of FIG. 1E with a constriction 502 along thelength of the wire 106-1. In some embodiments, the constriction 502 islocated along an edge of the superconducting layer 151 as shown in FIG.5A, while in other embodiments, the constriction 502 is located alongthe gap 152-1. In some embodiments, the superconducting circuit 501 doesnot include the constriction 502.

FIG. 5A shows the superconducting circuit 501 at a first time, similarto the circuit shown in FIG. 3A. At the first time, the current source104 is supplying a current 302 to the superconducting layer 151 and atleast a portion of the current 302 is flowing through each of the wires106 (e.g., 106-1, 106-2, 106-3, 106-4, and 106-5).

FIG. 5B shows the superconducting circuit 501 at a second time (that issubsequent to the first time). As shown in FIG. 5B, at the second time,the current source 104 is still supplying the current 302 and thecurrent source 102 is supplying an additional current 304 (optionallyvia wire 116).

FIG. 5C shows the superconducting circuit 501 at a third time (that issubsequent to the second time). As shown in FIG. 5C, at the third time,at least a portion of the wire 106-1 has transitioned from asuperconducting state to a non-superconducting state as denoted by theregion 506-1. The transition of the wire 106-1 is in response to thecurrent supplied to the wire 106-1 (e.g., a sum of the current 304 and aportion of the current 302 previously flowing through the wire 106-1)exceeding a threshold superconducting current for the wire 106-1 (e.g.,current between 0.5 μA and 10 μA). In some embodiments, the current 304from the current source 102 is adapted (e.g., selected) such that thetotal current supplied to the wire 106-1 (e.g., current 304 plus aportion of current 302) exceeds the threshold superconducting currentfor the wire 106-1.

In the non-superconducting state, the wire 106-1 has a non-zeroelectrical resistance and thus the current ceases to flow through thewire 106-1. Current that previously flowed through the wire 106-1 (e.g.,the current 304 from current source 102 and a portion of the current 302from current source 104) is redirected through the other wires 106(e.g., wires 106-2, 106-3, 106-4, and 106-5). In some embodiments, thecurrent source 102 continues to supply the current 304 after the wire106-1 has transitioned to the non-superconducting state, while in otherembodiments, the current source 102 ceases to supply the current 304after the wire 106-1 has transitioned to the non-superconducting state.

In the non-superconducting state (and/or during the transition from thesuperconducting state to the non-superconducting state), the non-zeroelectrical resistance of the wire 106-1 causes heat to be produced atwire 106-1. In accordance with some embodiments, the heat from the wire106-1 transfers to the wire 106-2 (e.g., the gap 152-1 is filled with athermally conductive material and/or the wire 106-1 and the wire 106-2are thermally coupled through a thermally conductive material locatedabove or below the wire 106-1 and the wire 106-2). In some embodiments,the heat from the wire 106-1 transfers to the wire 106-2 via the gap152-1. In accordance with some embodiments, the wire 106-1 and the wire106-2 are capacitively coupled via the gap 152-1 (e.g., in addition to,or instead of, the thermal coupling between the wire 106-1 and the wire106-2 based, for example, on the presence of the thermally conductivematerial in the gap 152-1). Therefore, energy transfers (e.g., currentflows) from the wire 106-1 to the wire 106-2 via capacitive chargingonce the wire 106-1 transitions to the non-superconducting state. FIG.5C shows heat and/or energy 508-1 transfer from the wire 106-1 to thewire 106-2 (e.g., heat transfer through thermal coupling and/or energytransfer through capacitive coupling).

FIG. 5D shows the superconducting circuit 501 at a fourth time (that issubsequent to the third time). As shown in FIG. 5D, at the fourth time,the wire 106-2 has transitioned from a superconducting state to anon-superconducting state as denoted by the region 506-2.

In some embodiments, the transition of the wire 106-2 is in response tothe current supplied to the wire 106-2 exceeding a thresholdsuperconducting current for the wire 106-2 (e.g., due to the additionalcurrent redirected from the wire 106-1). In some embodiments, thetransition of the wire 106-2 is in response to the heat and/or energytransfer 508-1 from the wire 106-1 (shown in FIG. 5C). In accordancewith some embodiments, the heat transfer from the wire 106-1 increases atemperature of the wire 106-2 above a threshold superconductingtemperature. In some embodiments, the energy transferred from the wire106-1 induces additional current for the wire 106-2 such that theportion of the current 302 flowing through the wire 106-2 (e.g., priorto, or in the absence of, any additional current redirected from thewire 106-1) exceeds a threshold superconducting current for the wire106-2, causing the wire 106-2 to transition to a non-superconductingstate.

In some instances, the threshold superconducting current for the wire106-2 is based on an operating temperature of the wire 106-2. Forexample, in some embodiments, when the operating temperature of the wire106-2 increases, the threshold superconducting current decreases suchthat the threshold superconducting current is exceeded with less currentflowing through the wire 106-2. Therefore, in accordance with someembodiments, the heat transfer 508-1 increases a temperature of the wire106-2 such that the portion of the current 302 flowing through the wire106-2 (e.g., prior to, or in the absence of, any additional currentredirected from the wire 106-1) exceeds a threshold superconductingcurrent (which has been reduced due to the increased temperature of thewire 106-2) for the wire 106-2, causing the wire 106-2 to transition toa non-superconducting state. In some embodiments, the wire 106-2transitions from the superconducting state to the non-superconductingstate based on a combination of the current supplied to the wire 106-2(e.g., additional current due to the redirection of the currentpreviously supplied to the wire 106-1 and/or the energy transferred fromthe wire 106-1 to the wire 106-2 via capacitive coupling) and the heattransferred from the wire 106-1 to the wire 106-2.

In the non-superconducting state (and/or during the transition from thesuperconducting state to the non-superconducting state), the non-zeroelectrical resistance of the wire 106-2 causes heat to be produced atwire 106-2. In accordance with some embodiments, the heat from the wire106-2 transfers to the wire 106-3. In accordance with some embodiments,the heat from the wire 106-2 transfers to the wire 106-3 via a thermallyconductive material (e.g., the gap 152-2 is filled with a thermallyconductive material and/or the wire 106-4 and the wire 106-5 arethermally coupled through a thermally conductive material located aboveor below the wire 106-4 and the wire 106-5). In accordance with someembodiments, the wire 106-2 and the wire 106-3 are capacitively coupledvia the gap 152-2 (e.g., in addition to, or instead of, the thermalcoupling between the wire 106-2 and the wire 106-3 based, for example,on the presence of the thermally conductive material in the gap 152-2).Therefore, energy transfers from the wire 106-2 to the wire 106-3 viacapacitive coupling. FIG. 5D shows heat and/or energy 508-2 transferfrom the wire 106-2 to the wire 106-3 (e.g., heat transfer throughthermal coupling and/or energy transfer through capacitive coupling).

FIG. 5E shows the superconducting circuit 501 at a fifth time (that issubsequent to the fourth time). As shown in FIG. 5E, at the fifth time,the wire 106-3 has transitioned from a superconducting state to anon-superconducting state as denoted by the region 506-3.

In some embodiments, the transition of the wire 106-3 is in response tothe current supplied to the wire 106-3 exceeding a thresholdsuperconducting current for the wire 106-3 (e.g., due to the additionalcurrent redirected from the wire 106-2). In some embodiments, thetransition of the wire 106-3 is in response to the heat and/or energytransfer 508-2 from the wire 106-2 (shown in FIG. 5D). In accordancewith some embodiments, the heat transfer 508-2 from the wire 106-2increases a temperature of the wire 106-3 above a thresholdsuperconducting temperature. In some embodiments, the energy transferredfrom the wire 106-2 induces additional current for the wire 106-3 suchthat the portion of the current 302 flowing through the wire 106-3(e.g., prior to, or in the absence of, any additional current redirectedfrom the wire 106-2) exceeds a threshold superconducting current for thewire 106-3, causing the wire 106-3 to transition to anon-superconducting state.

In some instances, the threshold superconducting current for the wire106-3 is based on an operating temperature of the wire 106-3. Forexample, in some embodiments, when the operating temperature of the wire106-3 increases, the threshold superconducting current decreases suchthat the threshold superconducting current is exceeded with less currentflowing through the wire 106-3. Therefore, in accordance with someembodiments, the heat transfer 508-2 increases a temperature of the wire106-3 such that the portion of the current 302 flowing through the wire106-3 (e.g., prior to, or in the absence of, any additional currentredirected from the wire 106-2) exceeds a threshold superconductingcurrent (which has been reduced due to the increased temperature of thewire 106-3) for the wire 106-3, causing the wire 106-3 to transition toa non-superconducting state. In some embodiments, the wire 106-3transitions from the superconducting state to the non-superconductingstate based on a combination of the current supplied to the wire 106-3(e.g., due to the redirection of the current previously supplied to thewire 106-2 and/or the energy transferred from the wire 106-2 to the wire106-3 via capacitive coupling) and the heat transferred from the wire106-2 to the wire 106-3.

In the non-superconducting state (and/or during the transition from thesuperconducting state to the non-superconducting state), the non-zeroelectrical resistance of the wire 106-3 causes heat to be produced atwire 106-3. In accordance with some embodiments, the heat from the wire106-3 transfers to the wire 106-4 (e.g., the gap 152-3 is filled with athermally conductive material and/or the wire 106-4 and the wire 106-5are thermally coupled through a thermally conductive material locatedabove or below the wire 106-4 and the wire 106-5). In some embodiments,the heat from the wire 106-3 transfers to the wire 106-4 via the gap152-3. In accordance with some embodiments, the wire 106-3 and the wire106-4 are capacitively coupled via the gap 152-3 (e.g., in addition to,or instead of, the thermal coupling between the wire 106-3 and the wire106-4 based, for example, on the presence of the thermally conductivematerial in the gap 152-3). Therefore, energy transfers from the wire106-3 to the wire 106-4 via capacitive coupling. FIG. 5E shows heatand/or energy 508-2 transfer from the wire 106-3 to the wire 106-4(e.g., heat transfer through thermal coupling and/or energy transferthrough capacitive coupling).

FIG. 5F shows the superconducting circuit 501 at a sixth time (that issubsequent to the fifth time). As shown in FIG. 5F, at the sixth time,the wire 106-4 has transitioned from a superconducting state to anon-superconducting state as denoted by the region 506-4.

In some embodiments, the transition of the wire 106-4 is in response tothe current supplied to the wire 106-4 exceeding a thresholdsuperconducting current for the wire 106-4 (e.g., due to the additionalcurrent redirected from the wire 106-3). In some embodiments, thetransition of the wire 106-4 is in response to the heat and/or energytransfer 508-2 from the wire 106-3 (shown in FIG. 5E). In accordancewith some embodiments, the heat transfer from the wire 106-3 increases atemperature of the wire 106-4 above a threshold superconductingtemperature. In some embodiments, the energy transferred from the wire106-3 induces additional current for the wire 106-4 such that theportion of the current 302 flowing through the wire 106-4 (e.g., priorto, or in the absence of, any additional current redirected from thewire 106-3) exceeds a threshold superconducting current for the wire106-4, causing the wire 106-4 to transition to a non-superconductingstate.

In some instances, the threshold superconducting current for the wire106-4 is based on an operating temperature of the wire 106-4. Forexample, in some embodiments, when the operating temperature of the wire106-4 increases, the threshold superconducting current decreases suchthat the threshold superconducting current is exceeded with less currentflowing through the wire 106-4. Therefore, in accordance with someembodiments, the heat transfer 508-3 increases a temperature of the wire106-4 such that the portion of the current 302 flowing through the wire106-4 (e.g., prior to, or in the absence of, any additional currentredirected from the wire 106-3) exceeds a threshold superconductingcurrent (which has been reduced due to the increased temperature of thewire 106-4) for the wire 106-4, causing the wire 106-4 to transition toa non-superconducting state. In some embodiments, the wire 106-4transitions from the superconducting state to the non-superconductingstate based on a combination of the current supplied to the wire 106-4(e.g., due to the redirection of the current previously supplied to thewire 106-3 and/or the energy transferred from the wire 106-3 to the wire106-4 via capacitive coupling) and the heat transferred from the wire106-3 to the wire 106-4.

In the non-superconducting state (and/or during the transition from thesuperconducting state to the non-superconducting state), the non-zeroelectrical resistance of the wire 106-4 causes heat to be produced atwire 106-4. In accordance with some embodiments, the heat from the wire106-4 transfers to the wire 106-5 (e.g., the gap 152-4 is filled with athermally conductive material and/or the wire 106-4 and the wire 106-5are thermally coupled through a thermally conductive material locatedabove or below the wire 106-4 and the wire 106-5). In some embodiments,the heat from the wire 106-4 transfers to the wire 106-5 via the gap152-4. In accordance with some embodiments, the wire 106-4 and the wire106-5 are capacitively coupled via the gap 152-2 (e.g., in addition to,or instead of, the thermal coupling between the wire 106-4 and the wire106-5 based, for example, on the presence of the thermally conductivematerial in the gap 152-2). Therefore, energy transfers from the wire106-4 to the wire 106-5 via capacitive coupling. FIG. 5F shows heatand/or energy 508-4 transfer from the wire 106-4 to the wire 106-5(e.g., heat transfer through thermal coupling and/or energy transferthrough capacitive coupling).

FIG. 5G shows the superconducting circuit 501 at a seventh time (that issubsequent to the sixth time). As shown in FIG. 5G, at the seventh time,the wire 106-5 has transitioned from a superconducting state to anon-superconducting state as denoted by the region 506-5.

In some embodiments, the transition of the wire 106-5 is in response tothe current supplied to the wire 106-5 exceeding a thresholdsuperconducting current for the wire 106-5 (e.g., due to the additionalcurrent redirected from the wire 106-4). In some embodiments, thetransition of the wire 106-5 is in response to the heat and/or energytransfer 508-3 from the wire 106-4 (shown in FIG. 5E). In accordancewith some embodiments, the heat transfer from the wire 106-4 increases atemperature of the wire 106-5 above a threshold superconductingtemperature. In some embodiments, the energy transferred from the wire106-4 induces additional current for the wire 106-5 such that theportion of the current 302 flowing through the wire 106-5 (e.g., priorto any additional current redirected from the wire 106-4) exceeds athreshold superconducting current for the wire 106-5, causing the wire106-5 to transition to a non-superconducting state.

In some instances, the threshold superconducting current for the wire106-5 is based on an operating temperature of the wire 106-5. Forexample, in some embodiments, when the operating temperature of the wire106-5 increases, the threshold superconducting current decreases suchthat the threshold superconducting current is exceeded with less currentflowing through the wire 106-5. Therefore, in accordance with someembodiments, the heat transfer 508-4 increases a temperature of the wire106-5 such that the portion of the current 302 flowing through the wire106-5 (e.g., prior to any additional current redirected from the wire106-4) exceeds a threshold superconducting current (which has beenreduced due to the increased temperature of the wire 106-5) for the wire106-5, causing the wire 106-5 to transition to a non-superconductingstate. In some embodiments, the wire 106-5 transitions from thesuperconducting state to the non-superconducting state based on acombination of the current supplied to the wire 106-5 (e.g., due to theredirection of the current previously supplied to the wire 106-4 and/orthe energy transferred from the wire 106-4 to the wire 106-5 viacapacitive coupling) and the heat transferred from the wire 106-4 to thewire 106-5.

In response to all of the wires 106 transitioning to thenon-superconducting state, current 308 (e.g., some or all of current302) from the current source 104 is directed (optionally through theresistor(s) 112) to the circuitry 114. In some embodiments, theresistance of the resistor(s) 112 is less than a combined resistance ofthe wires 106 when the wires are in the non-superconducting state, whichfacilitates a large portion of the current 308 to flow to the circuitry114.

As described above with respect to FIGS. 5A-5G, providing the inputcurrent to the first wire 106-1 causes a sequential transition of wires106-1 through 106-5 from superconducting states to non-superconductingstates, which in turn redirects current from the second current source104 to the circuitry 114. Typically, the current provided by the secondcurrent source 104 is greater than the current provided by the firstcurrent source 102 (e.g., the current provided by the second currentsource 104 is at least 5, 10, 50, or 100 times greater than the currentprovided by the first current source 102). Thus, the electronic systemsillustrated in FIGS. 1A-1D, 2A-2B, 3A-3G, 4, and 5A-5G operate as anamplifier (e.g., a current amplifier).

In some embodiments, as illustrated in FIGS. 3A-3G, the current source102 need not provide the input current continuously to initiate thecurrent amplification. Rather, in some embodiments, the input current isa current pulse (e.g., a pulse having a top-hat waveform) with durationsufficient to cause the sequential (or near sequential) cascade oftransitions of the wires 106. In some cases, the duration is less than atime required for the cascade transition to complete (e.g., the firstcurrent source ceases to provide the input current before one of thewires 106, such as wire 106-5, transitions into the non-superconductingstate). In some other embodiments, as illustrated in FIGS. 5A-5G, thecurrent source 102 provides an input current for the entire durationrequired for the cascade transition to complete (e.g., the first currentsource continues to provide the input current until after all of thewires 106 transition into the non-superconducting state).

FIGS. 6A-6B are block diagrams illustrating representative components ofa superconductor circuit in accordance with some embodiments. FIG. 6Ashows superconducting wires 604 (e.g., wires 106 in FIG. 1A or wires 136in FIG. 1C) adjacent to a thermally-conductive layer 602. In someembodiments, the thermally-conductive layer 602 is deposited on top ofthe wires 604. In some embodiments, the wires 604-1 are formed from asuperconducting layer deposited on top of the thermally-conductive layer602. In some embodiments, the thermally-conductive layer 602 is composedof a thermally-conductive, electrically-insulating material, such asdiamond or aluminum nitride. In some embodiments, thethermally-conductive layer 602 is configured to facilitate heat transferbetween the wires 604-1 (e.g., in a manner described previously withrespect to FIGS. 5A-5G). In accordance with some embodiments, the wires604-1 in FIG. 6A are separated from one another by air gaps.

FIG. 6B shows the superconducting wires 604 separated from one anotherby a thermally-conductive material 606. In some embodiments, thethermally-conductive material 606 is composed of a thermally-conductive,electrically-insulating material, such as diamond or aluminum nitride.In some embodiments the superconducting wires 604 are separated from oneanother by the thermally-conductive material 606 shown in FIG. 6B (e.g.,thermally-conductive material portions 606-1 and 606-2) and are alsoadjacent to the thermally-conductive layer 602 shown in FIG. 6A.

In some embodiments, the superconducting wires 604 are formed byremoving sections of a superconducting film (e.g., removing the gaps 152from the superconducting layer 151 shown in FIG. 1E). In someembodiments, after the sections are removed a thermally-conductivematerial is deposited on the superconducting film. In accordance withsome embodiments, depositing the superconducting film generates thethermally-conductive 606 and the thermally-conductive layer 602. In someembodiments, the thermally-conductive material, after being deposited,is etched back using any of a number of well-known processes to form aset of wires separated by thermally-conductive material.

FIGS. 7A-7C are cross-sectional diagrams illustrating a representativefabrication sequence for a superconducting wire in accordance with someembodiments. FIG. 7A shows application of a superconducting material 704on a substrate 702, and application of a protective layer 706 on thesuperconducting material 704. In some embodiments, the substrate is asilicon-based substrate, such as a silicon nitride (SiN) substrate. Insome embodiments, the substrate does not include an oxide layer, so asto reduce or prevent oxidation of the superconducting material 704. Insome embodiments, the superconducting material 704 is a niobium-basedsuperconducting material, such as niobium-germanium. In someembodiments, the superconducting material 704 comprises a thin-film ofniobium-germanium (e.g., a film having a thickness less than 100 nm, 50nm, or 20 nm). In some embodiments, the protective layer 706 includes apassivation layer, such as a passivation layer composed of aluminumnitride (AlN). In some embodiments, the protective layer 706 consistsessentially of a dielectric material. In some embodiments, theprotective layer 706 comprises an oxide layer. In some embodiments, theprotective layer 706 does not include an oxide layer, so as to reduce,inhibit, or prevent oxidation of the superconducting material 704. Insome embodiments, the protective layer 706 is a thin film (e.g., a thinhaving a thickness of less than 20 nm, 10 nm, 2 nm, or 1 nm).

FIG. 7B shows the addition of a resist layer 708 on the surface of theprotective layer 706. In some embodiments, the resist layer 708 iscomposed of a polymer. In some embodiments, the resist layer 708comprises a photo-resist layer and/or an electro-resist layer. In someembodiments, the resist layer 708 is deposited and then patterned, withFIG. 7B showing the result after the patterning process is complete. Forexample, as shown in FIG. 7B, the resist layer 708 covers only a portionof the protective layer 706. In some embodiments, the resist layer 708is applied to only select portion(s) of the protective layer 706 (e.g.,via the use of masks and the like). In some embodiments, the resistlayer 708 is applied to the protective layer 706 and then portions ofthe resist layer 708 are removed (e.g., by the application of photonsand/or electrons to cause cross-linking in portions of the resist layerfollowed by subsequent removal of photo resists that have not beencross-linked).

As also shown in FIG. 7B, the layers 708, 706, and 704 are exposed to anetching process 710 (e.g., dry etching or wet etching) in accordancewith some embodiments. The resist layer 708 is adapted to resist theetching process 710, while the protective layer 706 and thesuperconducting material 704 are not adapted to resist the etchingprocess, in accordance with some embodiments. In some embodiments, thesubstrate 702 is adapted to resist the etching process 710. Statedanother way, in some embodiments the etching process 710 is designed toselectively etch and thus remove the materials used to form theprotective layer 706 and the superconducting material 704, but not theresist layer 708 and substrate 702.

FIG. 7C shows the layers 708, 706, and 704 after application of theetching process 710. As shown in FIG. 7C, application of the etchingprocess 710 removes portions of the protection layer 706 and thesuperconducting material 704 that are not covered by the resist layer708. In some embodiments, the resist layer 708 is subsequently removed(e.g., via the application of a stripper, such as acetone,1-methyl-2-pyrrolidon, etc.). In some embodiments, the superconductingmaterial 704 shown in FIG. 7C comprises a superconducting wire (e.g., asuperconducting nanowire).

FIG. 8 is a cross-sectional diagram illustrating a representativelayering for a superconducting wire in accordance with some embodiments.FIG. 8 shows the superconducting wire 704 on the substrate 702 with theprotective layer 706 on top of the superconducting wire 704. FIG. 8 alsoshows application of a second protective layer 804 over thesuperconducting wire 704 (e.g., to the sides of the superconducting wire704 and on top of the protective layer 706). In some embodiments, thesecond protective layer 804 comprises a dielectric layer. In someembodiments, the second protective layer 804 consists essentially of adielectric material. In some embodiments, the second protective layer804 comprises an oxide layer. In some embodiments, the second protectivelayer 804 does not include an oxide layer, so as to inhibit oxidation ofthe superconducting material 704. In some embodiments, the secondprotective layer 804 is composed of aluminum nitride. In someembodiments, the second protective layer 804 is composed of a samematerial as the protective layer 706 (e.g., aluminum nitride). In someembodiments, the second protective layer 804 is a carbon-baseddielectric material.

In some embodiments, the second protective layer 804 is applied on topof a resist layer (e.g., resist layer 708) that covers the protectivelayer 706. In some embodiments, the protective layer 706 is removedprior to application of the protective layer 804, such that theprotective layer 804 is applied to a top surface of the superconductingwire 704. In some embodiments, the second protective layer 804 isapplied via a sputtering process (e.g., at temperatures greater than 300degrees Celsius, such as 400 degrees to 800 degrees Celsius). In someembodiments, the second protective layer 804 is a thin film (e.g., athin having a thickness of less than 20 nm, 10 nm, or 5 nm).

FIGS. 9A-9B show examples of a photonic system that can employ one ormore superconducting amplifiers in accordance with one or moreembodiments. In the embodiments shown in FIGS. 9A-9B, a superconductingcircuit, e.g., any of the superconducting circuits 100, 120, 130, 140,150, 200, 210 and or any of the arrangements shown in FIGS. 3A-5Gdescribed above can be employed as one or more amplifiers. Morespecifically, the FIGS. 9A-9B illustrate a heralded single photon sourcein accordance with one or more embodiments. Such a source can be usedwithin any system for which a source of single photons is useful, e.g.,within a quantum communications system and/or a quantum computer thatemploys entangled photons as the physical qubits.

Turning to FIG. 9A, a heralded single photon source 900 is illustratedin accordance with one or more embodiments. Thick black lines in thefigure represent optical waveguides and thin black lines representelectrical interconnects (e.g. wires that may be formed fromsuperconducting or non-superconducting materials). The system is ahybrid photonic/electrical circuit that includes a pumped photon pairgenerator 903, a wavelength division multiplexer (WDM) 905 (which is a1×2 WDM in this example), a superconducting photon detector 907, asuperconducting amplifier circuit 909, and an optical switch 909. One ormore components of the system can be housed in a cryogenic environment,such as a cryostat, held at a temperature that is lower than thethreshold temperature for superconductivity, as described above.

An input optical waveguide 913 optically couples a pump photon source(not shown) to photon pair generator 903. A pump photon 902 enters thepumped photon pair source 903 via input optical waveguide 913. For thesake of illustration, any photons illustrated here are depicted outsideof the waveguides, but one of ordinary skill will appreciate that in aphysical device, these photons will propagate within one or more guidedmodes of the waveguide. In some embodiments, the pumped photon pairsource 903 can include a nonlinear optical material that generates twooutput photons, referred to as idler photon 904 and signal photon 906from one or more input pump photons 902. For example, the pumped photonpair generator 903 can generate a pair of output photons using a processknown as spontaneous four wave mixing. The pair of output photons,signal photon 904 and idler photon 906, are typically generated havingdifferent wavelengths/frequencies, e.g., with the sum of the energies ofthe signal and idler equal to the energy of the pump photon. Aftergeneration, signal photon 904 and idler photon 906 are optically coupledto the input of WDM 905 via waveguide 908. Because they are differentwavelengths/frequencies, WDM 905 redirects each photon along a differentoutput waveguide, e.g., signal photon 904 is directed along theheralding waveguide path 913 and idler photon 906 is redirected alongthe switched output waveguide path 915. Which photon is directed towhich path is not critical and the path of the idler photon and signalphoton can be exchanged without departing from the scope of the presentdisclosure.

In this example, a superconducting photon detector 907, e.g., asuperconducting nanowire single photon detector, is optically coupled tothe heralding waveguide path 913 and can produce an electrical signal(e.g. a current pulse, also referred to as a photon heralding signal) inresponse to the detection of the signal photon 904. Because the signalphoton 904 and idler photon 906 were generated nearly simultaneously asa pair, the electrical signal generated by the photon detector 907signals (i.e., “heralds”) the presence of the idler photon 906 in theswitched waveguide path. The heralding signal is often a small amplitudecurrent signal, e.g., microamps or less, and can be provided to thesuperconducting amplifier circuit 909 where it is amplified to a largeroutput signal that can be used to more effectively drive any downstreamelectronic and/or photonic circuits. Referring momentarily to thevarious FIGS. 1-5 described above, the small heralding signalcorresponds to current source 102 that provides a small additionalcurrent to a superconducting circuit, e.g., superconducting circuit 100,120, 130, 140, 150, 200, 210 and or any of the arrangements shown inFIGS. 3A-5G, to drive the superconducting wires of the circuit into thenon-superconducting state, e.g., via the sequential (or near sequential)cascade effect described in more detail above. The amplified signal isthen provided to the optical switch 911 via output electrical signalline 914. Again, referring momentarily to the various FIGS. 1-5described above, the optical switch 911 shown in FIG. 9A corresponds tothe circuitry 114 of the superconducting circuit described above.Accordingly, the use of the superconducting amplifier circuit 909provides for a system that can drive higher current loads than would bethe case with photon detector 907 operating on its own. After beingswitched, the idler photon 915 is provided via output waveguide 919,e.g., for use in constructing a highly entangled resource state for usein a downstream optical quantum computing system (not shown).

FIG. 9B illustrates how several single photon sources similar to photonsource 900 can be multiplexed to increase the reliability of the photongeneration process. Such a system is beneficial because of thenon-deterministic nature of the conversion between the pump photon andthe photon pair in the photon pair generator 903. More specifically,because the photon pair generation process is a quantum mechanicalprocess, it is inherently probabilistic, and thus it is not guaranteedthat every pump photon that enters a photon pair generator 903 willresult in the generation of a photon pair at the output. In fact, insome instances, the photon pair creation can fail entirely. Thus, toimprove the reliability of the photon generation process, several singlephoton generators 900-1, 900-2, . . . , 900-n, each receiving its ownpump photon per generation cycle, can be arranged in parallel andoptically (and electrically) coupled to a N×1 switch 915, as shown. Aswith the heralded single photon source 900, each single photon generator900-1, 900-2, . . . , 900-n possesses, or has an output coupled to, acorresponding dedicated heralding electrical signal line 910-1, 910-2, .. . , 910-n, which can provide a heralding signal that informs adownstream circuit element of the successful generation of a photon bythat particular photon source. In some embodiments, the heraldingelectrical signal lines 910-1, 910-2, . . . , 910-n are electricallycoupled to the N×1 switch 915. N×1 switch 915 includes digital logicthat interprets the heralding electrical signals and switches the inputport of the N×1 switch 915 accordingly so as to provide the generatedidler photon to the output port 917. Thus, in this case, each photonsource 900 includes a superconducting amplifier circuit whose internalarrangement of current sources and parallel superconducting wiresprovides for enough amplification to drive the logic stage of the N×1switch. In other examples, a small signal logic circuit can be employedbefore the amplifier and N×1 switch. One of ordinary skill willappreciate that other arrangements are possible without departing fromthe scope of the present disclosure.

FIGS. 10A-10B show the results of a numerical simulation of asuperconducting circuit in accordance with some embodiments. Morespecifically, the plots show the transient current response of eachsuperconducting wire as well as the current response 1001 at a 50 ohmload that represents the input impedance of the circuitry 114 (e.g., asshown in FIG. 1A). The simulation includes a system having a parallelarrangement of 4 superconducting wires with an initial 1 microampcurrent pulse provided at the input, e.g., from current source 102 shownFIGS. 1A-1E, 2A-2B and 3A-3G. The numerical model includes both thermaland electrical dynamical models and was done using the SimulationProgram with Integrated Circuit Emphasis (SPICE) software package.

To establish a baseline comparison, FIG. 10A shows the transientelectrical response of a system having equal inductance wires, such aswould be the case for a parallel arrangement of four wires 106 eachhaving the same length. After the 1 micoamp current pulse from currentsource 102, shown here as line 1003, the current in the first wire(e.g., wire 106-1 in FIG. 1A), shown here as line 1005, begins to dropas this wire transitions to the non-superconducting state. At the sametime, the current in the remaining wires increases as the initialcurrent pulse is simultaneously redistributed to the remaining threewires. The current response of these three wires is completelyoverlapped on this chart, and appears as a single curve 1007.

FIG. 10B shows the same simulation but this time using a series of foursuperconducting wires (e.g., corresponding to wires 106-1 to 106-4, FIG.1A) that each have respectively increasing impedances (e.g., which couldbe achieved by increasing their respective lengths, as discussed abovein reference to FIGS. 1A-1E). In this example, the impedance doublesfrom wire to wire such that the last wire has 8 times the impedance ofthe first wire. FIG. 10B shows that each wire experiences a currentpulse in a cascaded sequence. In this case, the initial current pulse1003 first causes a normal transition in the first wire (e.g., 106-1)subsequently driving the current 1005 in the first wire (e.g., wire106-1) to redistribute to the second wire (e.g., wire 106-2, withcurrent in the second wire shown as curve 1009), then to the third wire(e.g., wire 106-3, with current in the third wire shown as curve 1011),and then to the fourth wire (e.g., wire 106-4, with current in thefourth wire shown as curve 1013). As already discussed above, anddescribed in further detail below, this sequential cascade effect isbeneficial because a large fraction of the input pulse current istransferred to each wire sequentially (rather than shared equallyamongst the wires), thereby providing for a more efficient way to driveeach wire to the non-superconducting state.

In light of these principles and embodiments, we now turn to certainadditional embodiments.

In accordance with some embodiments, an electrical system (e.g.,superconducting circuit 100) includes: (1) a first circuit having aplurality of superconducting wires (e.g., wires 106-1 through 106-5 inFIG. 1A) connected in parallel with one another, the superconductingwires including: (a) a first superconducting wire (e.g., wire 106-1,FIG. 1A) with a corresponding first threshold superconducting current;and (b) a second superconducting wire (e.g., wire 106-2, FIG. 1A); (2) asecond circuit (e.g., circuitry 114, FIG. 1A) connected in parallel tothe first circuit; (3) a first current source (e.g., the current source102, FIG. 1A) connected to the first superconducting wire and configuredto selectively supply a first current (e.g., current 304, FIG. 3B); (4)a second current source (e.g., current source 104, FIG. 1A) connected toa combination of the first circuit and the second circuit and configuredto supply a second current (e.g., current 302, FIG. 3A) so that theplurality of superconducting wires operate in a superconducting state(e.g., in the absence of additional current, such as the first current).Supplying the first current to the first superconducting wire with thefirst current source causes at least the first superconducting wire tocease to operate in the superconducting state (e.g., the firstsuperconducting wire transitions in the non-superconducting state) andsubsequently (e.g., after the first superconducting wire ceases tooperate in the superconducting state) causes the second superconductingwire to cease to operate in the superconducting state (e.g., the secondsuperconducting wire transitions in the non-superconducting state).

In some embodiments, at least a portion of the superconducting circuitconsists of the niobium-germanium. In some embodiments, thesuperconducting circuit consists essentially of a niobium-germaniumalloy. In some embodiments, the niobium-germanium includes niobium andgermanium in a ratio from 3:1 to 3.5:1 (e.g., Nb₃Ge).

In some embodiments, the first circuit includes one or more additionalcomponents, such as resistors, capacitors, and inductors. In someembodiments, such additional components are connected in series orparallel to the plurality of superconducting wires. In some embodiments,one or more additional components are connected in series or parallel toa respective superconducting wire. In some embodiments, the secondcurrent source is connected directly or indirectly to the combination ofthe first circuit and the second circuit. For example, one or moreadditional components (e.g., a resistor) may be located between thesecond current source and the combination of the first circuit and thesecond circuit.

In some embodiments, supplying the first current to the firstsuperconducting wire causes two or more of the superconducting wires(e.g., wires 106, FIG. 1A), other than the first superconducting wire,to sequentially cease to operate in a superconducting state subsequentto the first superconducting wire ceasing to operate in thesuperconducting state, thereby redirecting current to the secondcircuit. For example, FIGS. 3B-3G show that the wires 106-2 through106-5 sequentially transition from the superconducting state to thenon-superconducting state and the current from the second current sourceis redirected to the second circuit.

In some embodiments, a first portion of the second current, less thanthe first threshold superconducting current, is configured to flowthrough the first superconducting wire while the first current sourceforgoes supplying the first current (e.g., as shown in FIG. 3A, when nocurrent is provided by current source 102, a portion of current 302flows through wire 106-1). A combination of the first current and thefirst portion of the second current is greater than the first thresholdsuperconducting current (e.g., when current source 102 provides current304 as shown in FIG. 3B, a combination of the current 304 and the firstportion of the second current exceeds the first thresholdsuperconducting current).

In some embodiments, the second superconducting wire has a secondthreshold superconducting current. In some embodiments, the secondthreshold superconducting current is greater than the first thresholdsuperconducting current. In some embodiments, a second portion of thesecond current, less than the second threshold superconducting current,is configured to flow through the second superconducting wire while thefirst current source forgoes supplying the first current. In someembodiments, subsequent to the first superconducting wire ceasing tooperate in the superconducting state, a current flowing through thesecond superconducting wire increases from the second portion of thesecond current to above the second threshold superconducting current.This causes the second superconducting wire to cease to operate in thesuperconducting state. For example, FIG. 3D shows the wire 106-2 hastransitioned to the non-superconducting state in response to additionalcurrent redirected from the wire 106-1.

In some embodiments, supplying the first current to the firstsuperconducting wire (in addition to a portion of the second currentflowing through the first superconducting wire) causes allsuperconducting wires of the plurality of superconducting wires to ceaseto operate in the superconducting state such that at least the secondcurrent is supplied to the second circuit. For example, as shown inFIGS. 3B-3G, providing current 304 causes all of the wires 106 totransition into the non-superconducting state and the current 308 toflow toward the circuitry 114.

In some embodiments, in response to the first current, the plurality ofsuperconducting wires transition from the superconducting state to anon-superconducting state over a period of time between 10 ps and 100ps. In some embodiments, supplying the first current (e.g., to the firstsuperconducting wire) causes the plurality of superconducting wires tocease to operate in the superconducting state for a period of timebetween 10 ns to 100 ns (e.g., after 10 ns to 100 ns, the plurality ofsuperconducting wires returns to the superconducting state). In someembodiments, the first current is between 1 μA and 20 μA (e.g., currentbetween 5 μA and 10 μA). In some embodiments, the second current isbetween 5 μA and 100 μA (e.g., current between 10 μA and 50 μA).

In some embodiments, the plurality of superconducting wires ispositioned such that, in response to the first current supplied to thefirst superconducting wire, the plurality of superconducting wiressequentially transitions from the superconducting state to anon-superconducting state. For example, the wires in FIGS. 1A-1D arepositioned such that the wires will sequentially transition from thesuperconducting state to the non-superconducting state in response tocurrent supplied by the current source 102.

In some embodiments, (1) the first superconducting wire has a firstlength; and (2) a constriction is defined on the first superconductingwire so that the constriction narrows a width of the firstsuperconducting wire for a portion of the first length (e.g.,constriction 202, FIG. 2A). In some embodiments, the first thresholdsuperconducting current for the first superconducting wire is determinedbased at least in part on a representative size (e.g., a width) of theconstriction.

In some embodiments, the constriction reduces a thresholdsuperconducting current for the first superconducting wire by reducingthe width of at least a portion of the first superconducting wire.

In some embodiments, the constriction is sized such that a ratio of awidth of the first superconducting wire and the width of the firstsuperconducting wire minus a width of the constriction is equal to, orgreater than, a ratio of the first threshold superconducting current forthe first superconducting wire and the first current (e.g., a ratio of(i-a) a difference between a width of the first superconducting wire anda width of the constriction and (i-b) a width of the firstsuperconducting wire is equal to, or less than, a ratio of (ii-a) thefirst current and (ii-b) the first threshold superconducting current forthe first superconducting wire). For example, the constriction is sizedbased on the Equation 1 below:

$\begin{matrix}{\frac{{width}_{{wire}\; 1}}{{width}_{{wire}\; 1} - {width}_{constriction}} \geq \frac{I_{{wire}\; 1}}{I_{in}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where I_(wire1) is the threshold superconducting current for the firstwire (e.g., wire 106-1) without a constriction, the width_(wire1) is thesmallest width of the first wire without a constriction (e.g., width203, FIG. 2A), and width_(constriction) is the smallest width of thefirst wire with the constriction (e.g., width 205, FIG. 2A). An exampleI_(wire1) is between 0.5 μA and 10 μA. In some embodiments, theconstriction has a width at least as great as a coherence length of thefirst superconducting wire (e.g., 5 nm-10 nm).

In some embodiments, the constriction has a geometric shape, such as arectangle, a triangle, or a semicircle. For example, the constriction202 in FIG. 2A has a semicircle shape. In some embodiments, theconstriction has a non-geometric shape.

In some embodiments, the first current source is configured toselectively supply the first current at a location on the firstsuperconducting wire adjacent to the constriction. For example, thecurrent source 102 in FIG. 3B is positioned to supply the current 304 ata location corresponding to the wire 106-1. In some embodiments, thefirst current is supplied at a location such that the first currentflows toward the constriction when the first superconducting wireoperates in the superconducting state. In some embodiments, the locationon the first superconducting wire is deemed to be adjacent to theconstriction when a distance between the location on the firstsuperconducting wire and the constriction is 1 μm or less (e.g., 100 nmor less).

In some embodiments, each superconducting wire of the plurality ofsuperconducting wires comprises a respective portion of a thin filmsheet (e.g., a deposition layer, such as superconducting layer 118, FIG.1A), the thin film sheet defining a respective gap separating eachsuperconducting wire of the plurality of superconducting wires. Forexample, FIG. 1A shows the gap 108-1 separating the wire 106-1 and thewire 106-2. In some embodiments, the gaps comprise air gaps. In someembodiments, the gaps comprise one or more insulating materials. In someembodiments, the thin film has a width between 300 nm and 5 microns. Insome embodiments, the thin film has a length of 10 microns or greater.In some embodiments, the thin film has a thickness between 2 nm and 10nm. In some embodiments, the thin film sheet is composed of asuperconducting material, such as niobium or a niobium alloy.

In some embodiments, each respective gap comprises a rectangular, orsubstantially rectangular, cut-out portion of the thin film sheet. Insome embodiments, the gaps have widths between 20 nm and 100 nm. In someembodiments, a respective gap is deemed to have a substantiallyrectangular cut-out when the width and length of the respective gap varyby less than 2 nm, 5 nm, or 10 nm.

In some embodiments, the electronic system also includes a substrate(e.g., a silicon substrate) positioned to support the thin film. In someembodiments, the substrate comprises an insulating material, such assilicon dioxide. In some embodiments, the thin film is deposited on thesubstrate.

In some embodiments, (1) the first superconducting wire is positionedadjacent to a first edge (e.g., the left edge of the superconductinglayer 118, FIG. 1A) of the thin film sheet; and (2) the plurality ofsuperconducting wires is parallel, or substantially parallel, to thefirst edge of the thin film sheet. In some embodiments, the plurality ofsuperconducting wires is deemed to be substantially parallel to thefirst edge when an angle between the first edge and the length of eachrespective wire varies by less than 2 degrees, 5 degrees, or 10 degrees.

In some embodiments, the first current source (e.g., the input currentsource) is positioned adjacent to the first edge of the thin film sheetfor selectively supplying the first current to the first superconductingwire, and the second current source (e.g., the amplification currentsource) is positioned adjacent to a second edge (e.g., the top edge ofthe superconducting layer 118, FIG. 1A) of the thin film sheet forsupplying at least a portion of the second current (e.g., theamplification current) to the plurality of superconducting wires.

In some embodiments, the first current source is connected to the firstsuperconducting wire via a supply wire (e.g., wire 116, FIG. 1A)connected to the thin film at a location on the first edge of the thinfilm. In some embodiments, the supply wire has a width between 10 nm and200 nm.

In some embodiments, the first superconducting wire has a firstcharacteristic length and the second superconducting wire has a secondcharacteristic length. In some embodiments, the second characteristiclength is greater than the first characteristic length. In someembodiments, the second characteristic length is the same as the firstcharacteristic length. In some embodiments, a characteristic length of asuperconducting wire corresponds to a physical length of thesuperconducting wire. In some embodiments, when the superconducting wirehas an asymmetric shape having a first length and a second length (e.g.,one side is shorter than the opposite side as shown by wire 106-2 inFIG. 1A), the characteristic length is the shorter length, the longerlength, or an average of the first length and the second length.

In some embodiments, the plurality of superconducting wires furtherincludes a third superconducting wire (e.g., the wire 106-3, FIG. 1A)having a third characteristic length greater than the firstcharacteristic length and the second characteristic length, wherein thesecond superconducting wire is located between the first superconductingwire and the third superconducting wire. In some embodiments, thecharacteristic length of the superconducting wires increases linearly.In some embodiments, the characteristic length of the superconductingwires increases nonlinearly (e.g., exponentially). In some embodiments,the third superconducting wire corresponds to a third thresholdsuperconducting current that is greater than the second thresholdsuperconducting current.

In some embodiments, the plurality of superconducting wires includessuperconducting wires having increasing lengths. For example, the wires106 in FIG. 1A having increasing lengths from wire 106-1 to wire 106-5.In some embodiments and instances, having wires of increasing lengthsfacilitates a cascade effect across the wires by increasing a distanceredirected current must travel to reach the non-adjacent wire (e.g., asillustrated in FIG. 1B). In some embodiments, the lengths are between200 nm and 5 microns. In some embodiments, the plurality ofsuperconducting wires includes 5 or more superconducting wires. In someembodiments, the plurality of superconducting wires includes 10 or moresuperconducting wires. In some embodiments, the plurality ofsuperconducting wires includes 20 or more superconducting wires. In someembodiments, the plurality of superconducting wires includes 50 or moresuperconducting wires. In some embodiments, the plurality ofsuperconducting wires includes up to 5 superconducting wires. In someembodiments, the plurality of superconducting wires includes up to 10superconducting wires. In some embodiments, the plurality ofsuperconducting wires includes up to 20 superconducting wires. In someembodiments, the plurality of superconducting wires includes up to 50superconducting wires, but any number of wires may be employed withoutdeparting from the present disclosure.

Advantageously, employing superconducting wires having sequentiallyincreasing lengths (as a function of distance from the first currentsource) can facilitate a sequential (or near sequential) transitioningto the normal state of each of the wires of the device and thus reducesthe overall amount of additional current that needs to be provided totransition every wire of the plurality of wires to thenon-superconducting state. In some embodiments, this advantageous effectcan be caused by the fact that a superconducting wire's inductance isproportional to its length. For example, turning to FIG. 4, theinductance of the series combination of inductors 406 and 404(representing the first wire) is less than the inductance of inductor408 (representing the second wire) which is less than the inductance ofinductor 410 (representing the nth wire) and so on. Accordingly, becausethe inductance of the first wire is the lowest, in response to a currentpulse from the first current source (e.g., current source 102 shown inFIG. 1A), current will preferentially pass through the first wire only(or first few wires) due to their relatively low transient impedance,where the AC impedance of a single superconducting wire is dominated byits inductance, with the inductance Z being generally proportional toωL(I), where L is or corresponds to the inductance of thesuperconducting wire (which is generally current dependent, where Irepresents the current) and ω is or corresponds to a frequency (e.g.,primary frequency component) of the time varying current pulse.

Thus, after the first wire makes the transition to thenon-superconducting state, a majority of the additional current providedby the first current source will subsequently pass through the secondsuperconducting wire and may not be substantially shared amongst thethird, fourth, fifth, etc. wires due to their relatively higherimpedances. The sequential transitioning to the non-superconductingstate of each wire from shortest length (lowest inductance) to longestlength (largest inductance) is advantageous because the majority of theadditional current is routed through one (or only a few) lowestimpedance wire(s) at a time. Thus, the amount of additional currentneeded to trigger the sequential transitions of all the wires across thedevice (also referred to as the sequential cascade) does not stronglydepend on the number of parallel wires used in the device. However, theaddition of more parallel wires allows for a larger bias current to beprovided by the second current source, while still keeping this biassource far enough below the superconducting threshold current to avoidnoise induced issues that could lead to inadvertent transitions of oneor more wires to the non-superconducting state. Higher bias current fromthe second current source is preferred because it is this current thatis diverted to the output load of the additionally downstream circuitry,e.g., circuitry 114 described above. Thus, if the additional currentprovided by the first current source is I_(in) and the bias currentprovided by the second circuit is I_(bias) the overall gain g of thecircuit is approximately equal to I_(bias)/I_(in).

In contrast, in a device having a plurality of parallel wires of thesame length, the impedance of each wire is equal and thus, aftertransitioning the first wire, the additional current is spread in equalproportion among the remaining superconducting wires. Thus, to ensurethat the additional shared current is sufficient to exceed the thresholdcurrent in each remaining wire, the amount of additional current mustscale with the number of wires, e.g., a five-wire circuit will requirefive times as much additional current than a single wire circuit.Alternatively, the bias current supplied by the second current sourcecan be increased to bring the current in each wire closer to thethreshold current to insure triggering by a modest additional current,but as already noted above, the system becomes unstable and susceptibleto noise in such a case. Accordingly, in most practically sized systemsthat employ equal length parallel wires, there is an upper limit to thenumber of wires that can be employed, e.g., on the order of 10 wires.Furthermore, because the gain of the system scales with the number ofwires, the practical limit to the number of wires in the equal-lengthdesign also leads to a practical upper limit to the gain of such adevice. Accordingly, a circuit that employs a parallel arrangement ofsuperconducting wires having sequentially increasing lengths can operatemore stably and with higher gain than one with equal length wires.

In some embodiments, the plurality of superconducting wires includessuperconducting wires having substantially the same thickness. In someembodiments, all superconducting wires of the plurality ofsuperconducting wires have substantially the same thickness. In someembodiments, the thickness is between 2 nm and 10 nm. In someembodiments, the plurality of superconducting wires includes wires withtwo or more different thicknesses. For example, a first wire has athickness of 2 nm and a second wire has a thickness of 10 nm.

In some embodiments, the plurality of superconducting wires includessuperconducting wires having substantially the same width. In someembodiments, all superconducting wires of the plurality ofsuperconducting wires have substantially the same width. In someembodiments, the width is between 20 nm and 200 nm. In some embodiments,the plurality of superconducting wires includes wires with two or moredifferent widths. For example, a first wire has a width of 20 nm and asecond wire has a width of 100 nm. In some embodiments and instances,having wires of differing widths facilitates a cascade effect across thewires (e.g., as illustrated in FIGS. 3A-3G) as the superconductingthreshold current for each wire is based in part on the width.

In some embodiments, a first end of each superconducting wire of theplurality of superconducting wires is aligned with a first end of eachof the other superconducting wires of the plurality of superconductingwires. For example, in FIG. 1A the top of each wire 106 is aligned witheach other wire 106. In some embodiments, the first end of eachsuperconducting wire comprises an end positioned toward to the secondcurrent source. In some embodiments, the first end of eachsuperconducting wire comprises an end positioned away from the secondcurrent source. In some embodiments, the end located away from thesecond current source is positioned toward a ground (e.g., a groundplane).

In some embodiments, a midpoint of each superconducting wire of theplurality of superconducting wires is aligned with a midpoint of anothersuperconducting wire of the plurality of superconducting wires. In someembodiments, a midpoint of each superconducting wire of the plurality ofsuperconducting wires is aligned with a midpoint of each of the othersuperconducting wires of the plurality of superconducting wires. Forexample, in FIG. 1B the midpoint of each wire 126 is aligned with amidpoint of each other wire 126.

In some embodiments, the second circuit is a readout circuit configuredto measure current received from at least the second current source. Insome embodiments, the readout circuit is a voltage readout circuit. Insome embodiments, the second circuit is configured to have a resistanceless than a representative resistance of the plurality ofsuperconducting wires when the plurality of superconducting wires is notoperating in the superconducting state. In some embodiments, the readoutcircuit has a resistance of 50 ohms.

In accordance with some embodiments, a method includes: (1) providing anamplification current to a first circuit that includes a plurality ofsuperconducting wires connected in parallel with one another, theamplification current causing the plurality of superconducting wires tooperate in a superconducting state; (2) while the plurality ofsuperconducting wires are operating in the superconducting state,supplying an additional current to a first superconducting wire of theplurality of superconducting wires so that current supplied to the firstsuperconducting wire exceeds a first threshold superconducting currentof the first superconducting wire; (3) in response to supplying theadditional current to the first superconducting wire, transitioning thefirst superconducting wire from the superconducting state to anon-superconducting state; and (4) subsequent the transition of thefirst superconducting wire from the superconducting state to thenon-superconducting state: (a) sequentially transitioning the remainderof the superconducting wires of the plurality of superconducting wiresfrom the superconducting state to the non-superconducting state; and (b)directing the amplification current to a second circuit that isconnected in parallel to the first circuit.

In some embodiments, the method includes maintaining the plurality ofsuperconducting wires in a superconducting state at a temperature above3 Kelvin. In some embodiments, the plurality of superconducting wires ismaintained at a temperature above 3.5 Kelvin. In some embodiments, theplurality of superconducting wires is maintained at a target temperaturebetween 3.5 and 5 Kelvin.

In accordance with some embodiments, an electronic device includes aplurality of superconducting wires (e.g., the wires 136, FIG. 1C)connected in parallel with one another, the plurality of superconductingwires including: (1) a first superconducting wire having a firstthreshold superconducting current; and (2) a second superconducting wirehaving a second threshold superconducting current that is greater thanthe first threshold superconducting current.

In some embodiments: (1) the first superconducting wire (e.g., the wire106-1, FIG. 2B) has a first length; and (2) a constriction (e.g., theconstriction 204, FIG. 2B) is defined on the first superconducting wireso that the constriction narrows a width of the first superconductingwire for a portion of the first length.

In some embodiments, the first superconducting wire is connected to asupply wire (e.g., wire 116, FIG. 3B) for providing an input current.

In accordance with some embodiments, a method includes: (1) depositing athin film of a superconducting material (e.g., the superconducting layer118, FIG. 1A) over a substrate; and (2) removing (e.g., etching) one ormore (e.g., two or more) portions of the thin film (e.g., the gaps 108,FIG. 1A) to define a plurality of superconducting wires, the pluralityof superconducting wires including: (a) a first superconducting wire(e.g., the wire 106-1, FIG. 1A) with a corresponding first thresholdsuperconducting current; and (b) a second superconducting wire with acorresponding second threshold superconducting current that is greaterthan the first threshold superconducting current.

In some embodiments, removing the one or more portions of the thin filmdefines a constriction (e.g., the constriction 204, FIG. 2B) on thefirst superconducting wire. In some embodiments, removing the one ormore portions of the thin film defines a supply wire (e.g., the wire116, FIG. 2B) connected to the first superconducting wire.

In accordance with some embodiments, an electronic system includes: (1)a first circuit that includes a plurality of superconducting wires(e.g., the wires 106 in FIG. 1E) connected in parallel with one another,the plurality of superconducting wires including: (a) a firstsuperconducting wire (e.g., the wire 106-1) with a corresponding firstthreshold superconducting current; and (b) a second superconducting wire(e.g., the wire 106-2); (2) a second circuit connected in parallel tothe first circuit (e.g., the circuitry 114); (3) a first current source(e.g., the current source 102) coupled to the first superconducting wireand configured to selectively supply a first current; and (4) a secondcurrent source (e.g., the current source 104) coupled to a combinationof the first circuit and the second circuit and configured to supply asecond current such that the plurality of superconducting wires operatein a superconducting state, where a combination of the first current andthe second current exceeds the first threshold superconducting current.

In some embodiments, the system further includes a thermally-conductivematerial coupling the first superconducting wire and the secondsuperconducting wire (e.g., the thermally-conductive layer 602 in FIG.6A and/or the thermally-conductive material 606 in FIG. 6B). In someembodiments, the thermally-conductive material comprises an electricalinsulator. In some embodiments, the thermally-conductive materialcomprises Aluminum Nitride (AlN) and/or diamond. In some embodiments,the thermally-conductive material thermally couples the firstsuperconducting wire and the second superconducting wire. In someembodiments, the thermally-conductive material has a thermalconductivity above a predefined thermal conductivity threshold. In someembodiments, heat generated by the first superconducting wire istransferred to the second superconducting wire at least partiallythrough the thermally-conductive material, thereby causing the secondsuperconducting wire to cease to operate in the superconducting state asdescribed above with respect to FIGS. 5A-5G.

In some embodiments, the first superconducting wire and the secondsuperconducting wire comprise a first layer, and thethermally-conductive material comprises a second layer adjacent to thefirst layer (e.g., the thermally-conductive layer 602 in FIG. 6A).

In some embodiments, the thermally-conductive material is locatedbetween the first superconducting wire and the second superconductingwire (e.g., the thermally-conductive material 604 in FIG. 6B).

In some embodiments, the first superconducting wire is capacitivelycoupled to the second superconducting wire. In some embodiments, adistance between the first superconducting wire and the secondsuperconducting wire is selected to cause a current in the firstsuperconducting wire to induce a current in the second superconductingwire by capacitive coupling.

In some embodiments, supplying the first current to the firstsuperconducting wire with the first current source causes at least thefirst superconducting wire to cease to operate in the superconductingstate and subsequently cause the second superconducting wire to cease tooperate in the superconducting state. For example, the current 304supplied in FIG. 5B causes the first wire 106-1 to transition to anon-superconducting state (FIG. 5C) and subsequently causes the secondwire 106-2 to transition to the non-superconducting state (FIG. 5D).

In some embodiments, supplying the first current to the firstsuperconducting wire causes two or more superconducting wires of theplurality of superconducting wires, other than the first superconductingwire, to sequentially cease to operate in a superconducting statesubsequent to the first superconducting wire ceasing to operate in thesuperconducting state, thereby redirecting at least a portion of thesecond current to the second circuit. For example, the current 304supplied in FIG. 5B causes each of the wires 106 to transition to anon-superconducting state as shown in FIGS. 5D-5G.

In some embodiments, the two or more superconducting wires of theplurality of superconducting wires sequentially cease to operate in thesuperconducting state due, at least in part, to being capacitivelyand/or thermally coupled to the first superconducting wire.

In some embodiments: (1) the first superconducting wire has a firstlength; (2) a constriction (e.g., constriction 502 in FIG. 5A) isdefined on the first superconducting wire so that the constrictionnarrows a width of the first superconducting wire for a portion of thefirst length; and (3) the first threshold superconducting current forthe first superconducting wire is determined based at least in part on arepresentative size of the constriction.

In some embodiments, each superconducting wire of the plurality ofsuperconducting wires comprises a respective portion of a thin filmsheet, the thin film sheet defining a respective gap separating eachsuperconducting wire of the plurality of superconducting wires. Forexample, the superconducting layer 151 in FIG. 1E includes gaps 152 thatdefine wires 106.

In accordance with some embodiments, a method includes: (1) providing anamplification current (e.g., via the current source 104) to a firstcircuit that includes a plurality of superconducting wires (e.g., thewires 106) connected in parallel with one another; (2) while theplurality of superconducting wires are operating in a superconductingstate, supplying an additional current (e.g., via the current source102) to a first superconducting wire of the plurality of superconductingwires so that current supplied to the first superconducting wire exceedsa first threshold superconducting current of the first superconductingwire; (3) in response to supplying the additional current to the firstsuperconducting wire, transitioning the first superconducting wire fromthe superconducting state to a non-superconducting state; (4) subsequentthe transition of the first superconducting wire from thesuperconducting state to the non-superconducting state: (a)transitioning (e.g., sequentially) the remainder of the superconductingwires of the plurality of superconducting wires from the superconductingstate to the non-superconducting state; and (b) directing theamplification current to a second circuit that is connected in parallelto the first circuit (e.g., as illustrated in FIGS. 5A-5G). In someembodiments, the plurality of superconducting wires are thermally and/orcapacitively coupled to one another (e.g., as described above withrespect to FIGS. 5A-5G).

In some embodiments, the method further includes: (1) in conjunctionwith transitioning the first superconducting wire from thesuperconducting state to the non-superconducting state, generating heatwith the first superconducting wire; and (2) transferring at least aportion of the heat generated with the first superconducting wire to asecond superconducting wire of the plurality of superconducting wires(e.g., as shown by heat and/or energy transfer 508-1 in FIG. 5C). Insome embodiments, the transferred portion of the heat lowers a thresholdsuperconducting current of the second superconducting wire. In someembodiments, the transferred portion of the heat causes the secondsuperconducting wire to transition from the superconducting state to thenon-superconducting state (e.g., as illustrated in FIG. 5D).

In some embodiments, the method further includes, in conjunction withtransitioning the first superconducting wire from the superconductingstate to the non-superconducting state, inducing a displacement currentin a second superconducting wire of the plurality of superconductingwires. In some embodiments, the displacement current in the secondsuperconducting wire lowers a threshold superconducting current of thesecond superconducting wire. In some embodiments, the displacementcurrent in the second superconducting wire causes the secondsuperconducting wire to transition from the superconducting state to thenon-superconducting state.

In some embodiments, transitioning the remainder of the superconductingwires of the plurality of superconducting wires from the superconductingstate to the non-superconducting state comprises triggering a cascadeeffect in the plurality of superconducting wires due, at least in part,to thermal and/or capacitive coupling between adjacent ones of theplurality of superconducting wires.

In accordance with some embodiments, an electronic device includes: (1)a plurality of superconducting wires connected in parallel with oneanother, the plurality of superconducting wires including: (a) a firstsuperconducting wire (e.g., the wire 106-1) having a first thresholdsuperconducting current; and (b) a second superconducting wire (e.g.,the wire 106-2) having a second threshold superconducting current thatis greater than the first threshold superconducting current.

In some embodiments: (1) the first superconducting wire has a firstlength; and (2) a constriction (e.g., the constriction 502) is definedon the first superconducting wire so that the constriction narrows awidth of the first superconducting wire for a portion of the firstlength.

In some embodiments, the first superconducting wire is connected to asupply wire (e.g., the wire 116) for providing an input current (e.g.,from the current source 102). In some embodiments, the firstsuperconducting wire is positioned so as to be capacitively-coupled tothe second superconducting wire. In some embodiments, the firstsuperconducting wire is thermally-coupled to the second superconductingwire.

In accordance with some embodiments, a method includes: (1) depositing athin film of a superconducting material over a substrate; and (2)removing one or more portions of the thin film to define a plurality ofsuperconducting wires (e.g., the wires 106), the plurality ofsuperconducting wires including: (a) a first superconducting wire (e.g.,the wire 106-1) with a corresponding first threshold superconductingcurrent; and (b) a second superconducting wire (e.g., the wire 106-2)with a corresponding second threshold superconducting current that isgreater than the first threshold superconducting current.

In some embodiments, removing the one or more portions of the thin filmdefines a constriction (e.g., the constriction 502) on the firstsuperconducting wire. In some embodiments, removing the one or moreportions of the thin film defines a supply wire (e.g., the wire 116)connected to the first superconducting wire.

In some embodiments, the method further includes depositing athermally-conductive layer on the thin film (e.g., thethermally-conductive layer 602). In some embodiments, thethermally-conductive layer is electrically-insulating. In someembodiments, the first superconducting wire and the secondsuperconducting wire are positioned for thermal coupling and/or acapacitive coupling of the first superconducting wire and the secondsuperconducting wire.

In accordance with some embodiments, an electronic system includes: (1)a first circuit that includes a plurality of superconducting wiresconnected in parallel with one another (e.g., the wires 106 in FIG. 1A),where (a) each superconducting wire of the plurality of superconductingwires comprises a respective portion of a thin film (e.g., the thin film118), the thin film defining a respective gap separating eachsuperconducting wire of the plurality of superconducting wires (e.g.,the gaps 108) from a neighboring superconducting wire, and where (b) theplurality of superconducting wires includes a first superconducting wire(e.g., the wire 106-1) with a corresponding first thresholdsuperconducting current and a second superconducting wire (e.g., thewire 106-2); (2) a first current source (e.g., the current source 102)coupled to the first superconducting wire and configured to supply afirst current; (3) a second current source (e.g., the current source104) coupled to a first end of the first superconducting wire and afirst end of the second superconducting wire, the second current sourceconfigured to supply a second current such that the plurality ofsuperconducting wires operate in a superconducting state; and (4) asecond circuit (e.g., the circuit 114) connected in parallel to thefirst circuit and coupled to the second current source, where acombination of the first current and the second current exceeds thefirst threshold superconducting current.

In some embodiments: (1) the plurality of superconducting wires includesa third superconducting wire (e.g., the wire 106-3); (2) the firstsuperconducting wire and the second superconducting wire are separatedby a first gap (e.g., the gap 108-1) having a first end closest to thesecond current source and a second end furthest from the second currentsource; (3) the second superconducting wire and the thirdsuperconducting wire are separated by a second gap (e.g., the gap 108-2)having a first end closest to the second current source and a second endfurthest from the second current source; (4) a second end of the secondgap extends further than a second end of the first gap (e.g., as shownin FIG. 1A with gaps 108-1 and 108-2); and (5) the secondsuperconducting wire is configured such that, when the firstsuperconducting wire is in a non-superconducting state, a currentdensity in a portion of the second superconducting wire adjacent to thesecond end of the first gap exceeds a threshold superconducting currentdensity for the second superconducting wire, thereby transitioning thesecond superconducting wire to the non-superconducting state.

In accordance with some embodiments, a method includes: (1) providing anamplification current (e.g., via the current source 104, FIG. 1A) to afirst circuit that includes a plurality of superconducting wiresconnected in parallel with one another; (2) while the plurality ofsuperconducting wires are operating in a superconducting state,supplying an additional current (e.g., via the current source 102, FIG.1A) to a first superconducting wire of the plurality of superconductingwires so that current supplied to the first superconducting wire exceedsa first threshold superconducting current of the first superconductingwire; (3) in response to supplying the additional current to the firstsuperconducting wire, transitioning the first superconducting wire fromthe superconducting state to a non-superconducting state; and (4)subsequent to the transition of the first superconducting wire from thesuperconducting state to the non-superconducting state: (a) sequentiallytransitioning the remainder of the superconducting wires of theplurality of superconducting wires from the superconducting state to thenon-superconducting state; and (b) directing the amplification currentto a second circuit that is connected in parallel to the first circuit.

In some embodiments: (1) each superconducting wire of the plurality ofsuperconducting wires comprises a respective portion of a thin film, thethin film defining a respective gap separating each superconducting wireof the plurality of superconducting wires; (2) the first superconductingwire and the second superconducting wire are separated by a first gaphaving a first end closest to the second current source and a second endfurthest from the second current source; (3) the second superconductingwire and the third superconducting wire are separated by a second gaphaving a first end closest to the second current source and a second endfurthest from the second current source; and (4) transitioning theremainder of the superconducting wires from the superconducting state tothe non-superconducting state comprises redirecting current in a portionof the second superconducting wire adjacent to the second end of thefirst gap such that a current density in the portion exceeds a thresholdsuperconducting current density for the second superconducting wire,thereby transitioning the second superconducting wire to thenon-superconducting state.

In accordance with some embodiments, a method for fabricating asuperconducting wire includes: (1) depositing a layer ofniobium-germanium (e.g., superconducting material 204); (2) removing oneor more portions of the layer of niobium-germanium to define one or morenanowires (e.g., as shown in FIGS. 7B-7C); and (3) depositing aprotective layer over the one or more nanowires (e.g., protective layer804 in FIG. 8). In some instances, the protective layer reduces orprevents oxidation of niobium-germanium in the one or more nanowires. Insome embodiments, the protective layer is deposited after the one ormore portions of the layer of niobium-germanium are removed to definethe one or more nanowires. In some embodiments, the nanowires aredefined by a patterned resist layer deposited on top of the layer ofniobium-germanium. In some embodiments, a reactive ion etch process(e.g., a CF₄ reactive ion etch process) transfers the pattern of theresist layer to the niobium-germanium layer.

In some embodiments, the layer of niobium-germanium is deposited byphysical vapor deposition. In some embodiments, the layer ofniobium-germanium is deposited at a temperature between 400 and 800°Celsius. In some embodiments, the layer of niobium-germanium isdeposited by sputtering.

In some embodiments, the method further includes depositing a secondprotective layer over the layer of niobium-germanium (e.g., protectivelayer 706). In some embodiments, the second protective layer isdeposited before the one or more portions of the layer ofniobium-germanium are removed to define the one or more nanowires. Insome embodiments, removing the one or more portions of the layer ofniobium-germanium to define the one or more nanowires includes removingone or more corresponding portions of the second protective layer.

In some embodiments, the method further includes annealing the layer ofniobium-germanium and the second protective layer. In some embodiments,the layer of niobium-germanium and the second protective layer areannealed at a temperature between 800° and 1500° Celsius. In someembodiments, the layer of niobium-germanium and the second protectivelayer are annealed in a nitrogen gas or vacuum environment. In someembodiments, the layer of niobium-germanium is annealed independently ofthe second protective layer (e.g., without annealing second protectivelayer).

Although some of various drawings illustrate a number of logical stagesin a particular order, stages that are not order dependent may bereordered and other stages may be combined or broken out. While somereordering or other groupings are specifically mentioned, others will beobvious to those of ordinary skill in the art, so the ordering andgroupings presented herein are not an exhaustive list of alternatives.Moreover, it should be recognized that the stages could be implementedin hardware, firmware, software or any combination thereof.

It will also be understood that, although the terms first, second, etc.are, in some instances, used herein to describe various elements, theseelements should not be limited by these terms. These terms are only usedto distinguish one element from another. For example, a first currentcould be termed a second current, and, similarly, a second current couldbe termed a first current, without departing from the scope of thevarious described embodiments. The first current and the second currentare both currents, but they are not the same condition unless explicitlystated as such.

The terminology used in the description of the various describedembodiments herein is for the purpose of describing particularembodiments only and is not intended to be limiting. As used in thedescription of the various described embodiments and the appendedclaims, the singular forms “a”, “an” and “the” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. It will also be understood that the term “and/or” as usedherein refers to and encompasses any and all possible combinations ofone or more of the associated listed items. It will be furtherunderstood that the terms “includes,” “including,” “comprises,” and/or“comprising,” when used in this specification, specify the presence ofstated features, integers, steps, operations, elements, and/orcomponents, but do not preclude the presence or addition of one or moreother features, integers, steps, operations, elements, components,and/or groups thereof.

As used herein, the term “if” is, optionally, construed to mean “when”or “upon” or “in response to determining” or “in response to detecting”or “in accordance with a determination that,” depending on the context.Similarly, the phrase “if it is determined” or “if [a stated conditionor event] is detected” is, optionally, construed to mean “upondetermining” or “in response to determining” or “upon detecting [thestated condition or event]” or “in response to detecting [the statedcondition or event]” or “in accordance with a determination that [astated condition or event] is detected,” depending on the context.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive or tolimit the scope of the claims to the precise forms disclosed. Manymodifications and variations are possible in view of the aboveteachings. The embodiments were chosen in order to best explain theprinciples underlying the claims and their practical applications, tothereby enable others skilled in the art to best use the embodimentswith various modifications as are suited to the particular usescontemplated.

1. (canceled)
 2. A system, comprising: a plurality of superconductingwires connected in parallel with one another, the plurality ofsuperconducting wires including: a first superconducting wire; and asecond superconducting wire; a first current source coupled to the firstsuperconducting wire and configured to supply a first current inresponse to a trigger event; and a second current source coupled inseries with the parallel combination of the first superconducting wireand the second superconducting wire and configured to supply a secondcurrent; wherein the plurality of superconducting wires are configuredto, while receiving the second current, operate in a superconductingstate in the absence of the first current; wherein the firstsuperconducting wire is configured to, while receiving the secondcurrent, transition to a non-superconducting state in response to thefirst current; and wherein the second superconducting wire is configuredto, while receiving the second current, transition to anon-superconducting state in response to the first superconducting wiretransitioning to the non-superconducting state.
 3. The system of claim2, further comprising a thermally-conductive material coupling the firstsuperconducting wire and the second superconducting wire.
 4. The systemof claim 3, wherein the first superconducting wire and the secondsuperconducting wire comprise a first layer, and wherein thethermally-conductive material comprises a second layer adjacent to thefirst layer.
 5. The system of claim 3, wherein the thermally-conductivematerial is located between the first superconducting wire and thesecond superconducting wire.
 6. The system of claim 2, wherein the firstsuperconducting wire is capacitively coupled to the secondsuperconducting wire.
 7. The system of claim 2, wherein: supplying thefirst current to the first superconducting wire with the first currentsource causes at least the first superconducting wire to cease tooperate in the superconducting state and subsequently cause the secondsuperconducting wire to cease to operate in the superconducting state.8. The system of claim 2, wherein: supplying the first current to thefirst superconducting wire causes two or more superconducting wires ofthe plurality of superconducting wires, other than the firstsuperconducting wire, to sequentially cease to operate in asuperconducting state subsequent to the first superconducting wireceasing to operate in the superconducting state, thereby redirecting atleast a portion of the second current to the second circuit.
 9. Thesystem of claim 8, wherein the two or more superconducting wires of theplurality of superconducting wires sequentially cease to operate in thesuperconducting state due, at least in part, to being capacitivelyand/or thermally coupled to the first superconducting wire.
 10. Thesystem of claim 2, wherein: the first superconducting wire has a firstlength; a constriction is defined on the first superconducting wire sothat the constriction narrows a width of the first superconducting wirefor a portion of the first length.
 11. The system of claim 2, whereineach superconducting wire of the plurality of superconducting wirescomprises a respective portion of a thin film sheet, the thin film sheetdefining a respective gap separating each superconducting wire of theplurality of superconducting wires.
 12. An electronic device,comprising: a plurality of superconducting wires connected in parallelwith one another, the plurality of superconducting wires including: afirst superconducting wire having a first threshold superconductingcurrent; a second superconducting wire having a second thresholdsuperconducting current that is greater than the first thresholdsuperconducting current; and a circuit node coupled to a first end ofthe first superconducting wire and to a first end of the secondsuperconducting wire.